The only time I had grey screen is when I've had Docky set up with all my Firefox launchers and apps, but realized that I still had to keep Firefox launchers on the desktop, to activate them properly in Docky. With desktop icons set to no desktop icons in customize when you right click the desktop, will bring you back to a grey screen after booting back in.
Can you right click empty space on the desktop? Then left click customise, then left click Desktop Settings. The Desktop Layout box at the top should say
Show desktop icons on primary monitor only
If it says
Then you need to change it back to
Show desktop icons on primary monitor only
Could you please also in a Terminal type
Copy and paste everything you see back here please? Do not worry it tells us what hardware you're running and nothing else. It gives us a clue as to what could be the problem, with your apps suddenly closing.

On the picture of your Terminal, I see you have 7 flatpak apps and 6 snap packages. I'm wondering if it is any of those that are failing to stay open?